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The effective diffusion of Brownian particles in periodic potential has been a central topic in nonequilibrium statistical physcis. A classical result is the Lifson formula which provides the effective diffusion constant in periodic…

Statistical Mechanics · Physics 2026-01-22 Sang Yang , Zhixin Peng

The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the…

Analysis of PDEs · Mathematics 2014-05-13 Arnaud Debussche , Sylvain De Moor , Julien Vovelle

We provide a rigorous derivation of the brownian motion as the hydrodynamic limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0,$ in the…

Analysis of PDEs · Mathematics 2015-02-25 Thierry Bodineau , Isabelle Gallagher , Laure Saint-Raymond

We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…

Mathematical Physics · Physics 2015-04-23 Patrik L. Ferrari , Herbert Spohn , Thomas Weiss

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…

Statistical Mechanics · Physics 2022-11-23 I. G. Marchenko , A. Zhiglo , V. Aksenova , V. Tkachenko , I. I. Marchenko , J. Łuczka , J. Spiechowicz

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…

Statistical Mechanics · Physics 2016-08-03 Shaked Regev , Niels Grønbech-Jensen , Oded Farago

A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…

Analysis of PDEs · Mathematics 2016-06-23 Michele Coghi , Franco Flandoli

Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…

Chaotic Dynamics · Physics 2009-11-07 Hidetsugu Sakaguchi

We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…

Dynamical Systems · Mathematics 2012-03-20 Georg Schöchtel

We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple intrinsic models for the motion of a massive point particle in a fixed causal set…

General Relativity and Quantum Cosmology · Physics 2009-11-25 Fay Dowker , Lydia Philpott , Rafael Sorkin

The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…

Mathematical Physics · Physics 2017-03-23 Maria Bruna , S. Jonathan Chapman

Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…

Probability · Mathematics 2024-11-07 Christopher Lutsko , Balint Toth

In this work, we focus on the behavior of a single passive Brownian particle in a suspension of passive particles with short-range repulsive interactions and a larger self-diffusion coefficient. While the forces affecting the…

Statistical Mechanics · Physics 2023-04-26 Deborah Schwarcz , Stanislav Burov

Diffusion coefficient usually decreases when friction increases. We analyze the opposite behavior in the paradigmatic system consisting of an inertial Brownian particle moving in a symmetric spatially periodic potential and driven by an…

Statistical Mechanics · Physics 2025-03-31 I. G. Marchenko , I. I. Marchenko , V. Aksenova , J. Łuczka , J. Spiechowicz

Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…

Probability · Mathematics 2025-07-23 Christian Bender , Yana A. Butko , Mirko D'Ovidio , Gianni Pagnini

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…

Probability · Mathematics 2015-08-24 Zsolt Pajor-Gyulai , Michael Salins

The purpose of the article is to address the limiting behavior of the solutions of stochastic differential equations driven by a pointy $d$-dimensional gradient as the intensity of the underlying Brownian motion tends to $0$. By pointy…

Probability · Mathematics 2019-09-20 François Delarue , Mario Maurelli

In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present…

Mathematical Physics · Physics 2015-11-17 Jens Marklof , Balint Toth

Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…

Materials Science · Physics 2009-09-29 Peter. Kotelenez , Marshall J. Leitman , J. Adin Mann

Diffusion behavior of Brownian particles in confined spaces was studied for the displacements notably shorter than the confinement size. The confinements, resembling structure of porous solids, were modeled using a spatially-varying…

Disordered Systems and Neural Networks · Physics 2016-11-24 Daniel Schneider , Rustem Valiullin , Nail Fatkullin